# Identification techniques when $E(u_i|\text{do}(X_i))\not=0$

In this article Chen & Pearl make the following 2 statements:

• "Identification techniques are available for models in which X is far from satisfying $$E(u_i|X_i)=0$$" in response to Stock & Watson's sentence: "In observational data, X is not randomly assigned in an experiment. Instead, the best that can be hoped for is that X is as if randomly assigned, in the precise sense that $$E(u_i|X_i)$$=0"

• "There are many techniques that allow unbiased estimation of causal
effects even when other factors are not held fixed
" in response to Wooldridge's sentence: "If other factors are not held fixed, then we cannot know the causal effect of a price change on quantity demanded."

Can someone list the techniques they are referring to?

• Did you miss $\text{do}(\cdot)$ in the body? Jan 14 at 17:50
• Good question, Richard. In the text, this is a quote of Chen & Pearl who are using the Economists' speak of $E(u_i|X_i)$ to really refer to $E(u_i|do(X_i))$ Jan 14 at 17:54
• Instrumental variables and difference-in-differences come to mind. Each requires a different assumption to identify the effect.
– Noah
Jan 14 at 18:18
• @ColorStatistics, I meant the discrepancy between the title and the body. Is it intentional? (I now see the quote in the body is accurate.) Jan 14 at 18:33
• @RichardHardy: Yes, it is intentional. The title is the way Chen & Pearl would have written it (and the way perhaps it is time Econometrics books write it), while body has exact quotes from textbooks. Jan 15 at 8:55